Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C11 ⋊ #1274 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=e,c^2=f,d^2=g,b^a=bc,e^a=ef,h^a=h^10,d^b=df244 conjugacy classes — view the full character table.
| maximal subgroup of | #14640548, #14640549, #14640586, … |
| maximal normal subgroup of | #14640548, #14640549, #14640586, … |
| maximal quotient of | C11⋊#7014, #14640305, #14640307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2339);